Say whether the l'Hospital's rule applies. If it does, use it to evaluate the given limit. If not, use some other method
limit x tends -1
(x^2+5x+4)/(x^2+x)

Question

Say whether the l'Hospital's rule applies. If it does, use it to evaluate the given limit. If not, use some other method
limit x tends -1
(x^2+5x+4)/(x^2+x)

amit69 · Answer

I found out that L' Hospital rule applies but cannot evaluate the limit

eliesaab · Answer

This limit can be evaluated using two different methods
$$
\frac{x^2+5 x+4}{x^2+x}=\frac{(x+1) (x+4)}{x (x+1)}=\frac{x+4}{x}\to -3
$$
as x goes to -1

eliesaab · Answer

The other method is to use L'Hospital Rule
$$
\lim_{x->-1} \frac{x^2+5 x+4}{x^2+x}=\lim_{x->-1}\frac {2x+5}{2x+1}=\frac 3{-1}=-3
$$

3mar · Answer

I thank you in person, @eliesaab!
Really it is helpful for me!

Thank you very much.

eliesaab · Answer

You are very welcome  @3mar

3mar · Answer

Thank you for good explanation.
You are Awesome, @eliesaab!